81.15.8 problem 19-9

Internal problem ID [21716]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-9
Date solved : Thursday, October 02, 2025 at 08:01:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 45

ode:=(x-1)^2*diff(diff(y(x),x),x)-4*(x-1)*diff(y(x),x)-14*y(x) = x^3-3*x^2+3*x-8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{\left (x -1\right )^{2}}+\left (x -1\right )^{7} c_1 -\frac {x \left (x^{4}-5 x^{3}+10 x^{2}-20 x +25\right )}{20 \left (x -1\right )^{2}} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 52

ode=(x-1)^2*D[y[x],{x,2}]-4*(x-1)*D[y[x],x]-14*y[x] ==x^3-3*x^2+3*x-8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-9 x^5+45 x^4-90 x^3+180 x^2-225 x+180 c_1 (x-1)^9+25+180 c_2}{180 (x-1)^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + 3*x**2 - 3*x + (x - 1)**2*Derivative(y(x), (x, 2)) - (4*x - 4)*Derivative(y(x), x) - 14*y(x) + 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3 + x**2*Derivative(y(x), (x, 2)) + 3*x**2 - 2*x*Derivative(y(x), (x, 2)) - 3*x - 14*y(x) + Derivative(y(x), (x, 2)) + 8)/(4*(x - 1)) cannot be solved by the factorable group method